A Quantum Light Source for Light-Matter Interaction by Xingxing Xing A thesis submitted in ...

195 Pages·2013·2.82 MB·English

A Quantum Light Source for Light-Matter Interaction
by
Xingxing Xing
A thesis submitted in conformity with the requirements
for the degree of Doctor of Philosophy
Graduate Department of Physics
University of Toronto
Copyright ⃝c 2013 by Xingxing Xing
Abstract
A Quantum Light Source for Light-Matter Interaction
Xingxing Xing
Doctor of Philosophy
Graduate Department of Physics
University of Toronto
2013
I present in this thesis the design, implementation and measurement results of a nar-
rowband quantum light source based on cavity-enhanced Parametric Down-Conversion
(PDC). Spontaneous Parametric Down-Conversion (SPDC) is the workhorse in the field
of optical quantum information and quantum computation, yet it is not suitable for appli-
cations where deterministic nonlinearities are required due to its low spectral brightness.
By placing the nonlinear crystal inside a cavity, the spectrum of down-conversion is ac-
tively modified, such that all the non-resonant modes of down-conversion experience de-
structive interference, while the resonant mode sees constructive interference, resulting in
great enhancement in spectral brightness. I design and construct such a cavity-enhanced
down-conversion source with record high spectral brightness, making it possible to use
cold atoms as the interaction medium to achieve large nonlinearity between photons.
The frequency of the photons is tunable and their coherence time is measured to be on
the order of 10 nanoseconds, matching the lifetime of the excited state of typical alkali
atoms. I characterize extensively the output of the source by measuring the second-order
correlation function, quantifying two-photon indistinguishability, performing quantum
state tomography of entangled states, and showing different statistics of the source.
The unprecedented long coherence time of the photon pairs has also made possible
the encoding of quantum information in the time domain of the photons. I present a
theoretical proposal of multi-dimensional quantum information with such long-coherence-
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time photons and analyze its performance with realistic parameter settings. I implement
this proposal with the quantum light source I have built, and show for the first time
that a qutrit can be encoded in the time domain of the single photons. I demonstrate
the coherence is preserved for the qutrit state, thus ruling out any classical probabilistic
explanation of the experimental data. Such an encoding scheme provides an easy access
to multi-dimensional systems and can be used as a versatile platform for many quantum
information and quantum computation tasks.
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To my family,
for their unwavering support.
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Acknowledgements
I feel fortunate to have the opportunity to tackle some challenging problems during my
study at the University of Toronto. The last few years has been focused and intense
period of my life. Much of what I learned I will carry through the rest of my life.
There are many people I want to thank who have made this an delightful and rewarding
experience.
First and foremost, I want to thank my thesis supervisor, Aephraim Steinberg, with-
out whom this work will not be possible. His breadth of knowledge and vision has made
many discussions enjoyable and fruitful. He has a unique way of approaching and under-
standing problems intuitively, which for many times shows me the beauty of physics. He
has been very supportive and allows us to pursue our own interests, which for me was
to work on a project bridging Aephraim’s two existing labs. I started my work in the
lab independently, and I am grateful to Rob Adamson for being a knowledgable mentor
in the lab and very patient in answering my questions, no matter how dumb they are.
Mirco Siercke has also been very helpful through the early times of the project. In 2007,
I was fortunate to won a fellowship that supported me to visit Morgan Mitchell’s group
at ICFO in Spain for three months. Morgan was a valuable source of knowledge and I
was learning many experimental techniques from him. His group members also provided
great help. In particular, I have spent many time in the lab with Florian Wolfgramm dis-
cussing problems, aligning optics and taking data. Florian also visited us in the summer
of 2008 which was again a very productive period. I also owe many thanks to other mem-
bers of Aephraim’s group. Amir Feizpour and Greg Dmochowski have helped numerous
times in debugging and understanding the experiments. I also spent many hours in the
lab with Yasaman Soudagar on the cluster quantum computation project, though the
work is not presented in this thesis. Alex Hayat, our newly joint postdoc, is relentlessly
resourceful in solving many theoretical and experimental issues. Chris Ellenor, Rockson
Chang, Chao Zhuang, Krister Shalm, Lee Rozema ,Dylan Mahler, Chris Pual, and the
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rest of the group members have made the lab an interesting and productive place. I also
want to thank Alan Stummer for his expertise in electronics, and for his help in making
sure the circuits are doing what they were supposed to do.
I want to thank my parents for their unconditional support, and my brothers, Jian
and Kang, for their support in my decision of going to graduate school in Canada. I can
still remember lessons of science and life from them when I was a kid. I also want to
thank many friends who has made my life enjoyable beside academic research. Finally,
I want to thank my girlfriend, Wenwen Jiang, for keeping me grounded in the last year,
and for her supports that have made bad times bearable, and good times more enjoyable.
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Contents
1 Introduction 1
2 Concepts and techniques 5
2.1 Weak-nonlinearity-based quantum computation . . . . . . . . . . . . . . 5
2.1.1 The proposal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Ultracold atoms as a nonlinear medium . . . . . . . . . . . . . . . 7
2.2 Optical cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Cavity basics and cavity enhancement . . . . . . . . . . . . . . . 9
2.2.2 Transmission of a cavity . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Mode-matching and alignment of cavity . . . . . . . . . . . . . . 16
2.3 Frequency stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1 Pound-Drever-Hall locking techniques . . . . . . . . . . . . . . . . 20
2.3.2 Spectroscopic features . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.3 Laser linewidth narrowing . . . . . . . . . . . . . . . . . . . . . . 23
2.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.1 Phase measurement . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4.2 Wave plate calibration . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.3 Electro-optic modulators . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Photon detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5.1 Photon counting . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
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2.5.2 Practical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6 Quantum correlations and measurements . . . . . . . . . . . . . . . . . . 34
2.6.1 Coincidence detection . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.6.2 Correlation measurements . . . . . . . . . . . . . . . . . . . . . . 37
2.6.3 Entanglement and non-classicality . . . . . . . . . . . . . . . . . . 39
2.6.4 Quantum state tomography . . . . . . . . . . . . . . . . . . . . . 40
3 The quantum light source 42
3.1 Classical light source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2 Spontaneous parametric down-conversion . . . . . . . . . . . . . . . . . . 43
3.2.1 Phase-matching conditions . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2 Quasi-phase matching . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Optical parametric oscillators . . . . . . . . . . . . . . . . . . . . . . . . 50
3.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.3.2 Cavity enhancement . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.4 Cavity design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.1 Compensation schemes . . . . . . . . . . . . . . . . . . . . . . . . 55
3.4.2 Design considerations . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5 Output characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5.1 Time-resolved coincidence counting . . . . . . . . . . . . . . . . . 65
3.5.2 Indistinguishable photon pairs . . . . . . . . . . . . . . . . . . . . 67
3.5.3 Quantum state tomography . . . . . . . . . . . . . . . . . . . . . 74
3.5.4 Pump power dependence . . . . . . . . . . . . . . . . . . . . . . . 79
3.6 Spectral Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.6.1 Filter cavity design . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.6.2 Narrowband photons after filtering . . . . . . . . . . . . . . . . . 85
3.7 Measurement of quantum statistics . . . . . . . . . . . . . . . . . . . . . 87
3.7.1 Poisson statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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nd
3.7.2 Photon bunching - 2 -order correlation . . . . . . . . . . . . . . 88
rd
3.7.3 Photon bunching - 3 -order correlation . . . . . . . . . . . . . . . 95
3.7.4 Photon anti-bunching . . . . . . . . . . . . . . . . . . . . . . . . . 106
4 Time-domain multidimentional quantum information 109
4.1 Time-domain encoding and decoding . . . . . . . . . . . . . . . . . . . . 110
4.1.1 State preparation and detection . . . . . . . . . . . . . . . . . . . 110
4.1.2 Two encoding schemes . . . . . . . . . . . . . . . . . . . . . . . . 113
4.1.3 Linear-phase-ramp encoding . . . . . . . . . . . . . . . . . . . . . 116
4.2 Performance analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.1 Error rate analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.2.2 Channel capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.3.1 Detection cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
4.3.2 Quantum state reconstruction . . . . . . . . . . . . . . . . . . . . 137
4.3.3 Characterization of a quantum channel . . . . . . . . . . . . . . . 141
5 Conclusion 147
5.1 Major results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
A Propotional-Integral-Derivative (PID) controller 150
B Time-to-digital converter and coincidence counting 154
Bibliography 159
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List of Figures
2.1 Quantum Non-Demonition (QND) measurement with Cross-Kerr effect. . 6
2.2 Different cavity geometries . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Multiple reflection and transmission in a cavity. . . . . . . . . . . . . . . 11
2.4 Cavity resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5 Cavity transmission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Measurement of cavity impedance mismatch . . . . . . . . . . . . . . . . 16
2.7 Gaussian beam in a cavity . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.8 Beam propagation and mode matching to a cavity . . . . . . . . . . . . . 18
2.9 Different cavity modes captured by a camera. . . . . . . . . . . . . . . . 19
2.10 Simulation of Pound-Drever-Hall locking technique . . . . . . . . . . . . 22
2.11 Pound-Drever-Hall locking technique . . . . . . . . . . . . . . . . . . . . 22
2.12 Saturated absorption spectroscopy . . . . . . . . . . . . . . . . . . . . . . 24
2.13 Error signal from a cavity with Pound-Drever-Hall (PDH) technique . . . 25
2.14 Calibration of phase measurement . . . . . . . . . . . . . . . . . . . . . . 27
2.15 Calibration setup for the phase and amplitude Electro-Optic Modulators
(EOMs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.16 Calibration data for phase and amplitude EOM . . . . . . . . . . . . . . 32
2.17 Photon detection efficiency of single photon detectors . . . . . . . . . . . 33
2.18 Schematic for the Hanbury-Brown-Twiss (HBT) effect . . . . . . . . . . . 38
3.1 Schematic of frequency stabilized laser system . . . . . . . . . . . . . . . 43
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